Game of Trojans: A Submodular Byzantine Approach
This addresses security vulnerabilities in ML models for applications like autonomous systems, but it is incremental as it builds on existing Trojan attack and detection research.
The paper tackles the problem of Trojan attacks in machine learning models by determining the minimal fraction of samples needed for a Trojan trigger and proving that an adaptive adversary can bypass detection with probability one, showing that only a very small fraction of samples is required for high accuracy on both Trojan and clean samples.
Machine learning models in the wild have been shown to be vulnerable to Trojan attacks during training. Although many detection mechanisms have been proposed, strong adaptive attackers have been shown to be effective against them. In this paper, we aim to answer the questions considering an intelligent and adaptive adversary: (i) What is the minimal amount of instances required to be Trojaned by a strong attacker? and (ii) Is it possible for such an attacker to bypass strong detection mechanisms? We provide an analytical characterization of adversarial capability and strategic interactions between the adversary and detection mechanism that take place in such models. We characterize adversary capability in terms of the fraction of the input dataset that can be embedded with a Trojan trigger. We show that the loss function has a submodular structure, which leads to the design of computationally efficient algorithms to determine this fraction with provable bounds on optimality. We propose a Submodular Trojan algorithm to determine the minimal fraction of samples to inject a Trojan trigger. To evade detection of the Trojaned model, we model strategic interactions between the adversary and Trojan detection mechanism as a two-player game. We show that the adversary wins the game with probability one, thus bypassing detection. We establish this by proving that output probability distributions of a Trojan model and a clean model are identical when following the Min-Max (MM) Trojan algorithm. We perform extensive evaluations of our algorithms on MNIST, CIFAR-10, and EuroSAT datasets. The results show that (i) with Submodular Trojan algorithm, the adversary needs to embed a Trojan trigger into a very small fraction of samples to achieve high accuracy on both Trojan and clean samples, and (ii) the MM Trojan algorithm yields a trained Trojan model that evades detection with probability 1.